Excess Noise in TESs A comparison between theories.

Transcription

1 Space Research Centre Excess Noise in TESs A comparison between theories Daniel Brandt, George W. Fraser, Stephen Smith

2 Introduction Excess Noise Theories Experiments have shown that the noise power spectrum of practical TES can not be explained by conventional noise sources. The excess noise observed appears to originate from inside the TES and behaves as a constant voltage noise source (Takei et al.). We will contrast and compare two theories describing the excess noise Univsersidad Autonoma de Madrid (uam), University of Leicester Space Research Centre (SRC), Y. Takei et al., NIM A 523 (2004) 134

3 Introduction Excess Noise Theories Phase Slip Shot Noise Vortices moving perpendicular to bias current responsible for noise (Fraser) Vortex motion creates change in superconducting order parameter φ Percolation Noise The superconducting film consists of a number of domains of area (coherence length) 2 (Lindeman et al.) In the transition these domains fluctuate randomly between their SC and normal states If dφ/dt is not zero a voltage appears across the TES If by coincidence a set of SC domains forms a cluster linking both ends of the TES the device resistance is reduced until the cluster dissolves M.A. Lindeman et al., NIM A 559 (2006) 715 G.W. Fraser, NIM A 523 (2004) 234

4 Noise vs. Resistance Several experimenters report the excess noise to scale as R -1 (Lindeman et al., Takei et al.) Phase Slip Shot Noise Percolation Noise i n = S R v i n = S RS R ( rs f ) ( VI) 1 2 i n! R!0.9 i n " R RS for a 2D Film (Kiss et al.) PSSN meets the R -1 requirement Percolation Noise approximately meets the R -1 requirement M.A. Lindeman et al., NIM A 559 (2006) 715 Y. Takei et al., NIM A 523 (2004) 134 L.B. Kiss et al., Phys. Rev. Lett. 71 (1993) 2817

5 Magnetic Field Dependence of Noise To date, no quantitative predictions are made about the relation between excess noise and magnetic field by either theory.

6 Magnetic Field Dependence of PSSN Using the PSSN equations derived by Fraser, 2003 and using the vortex dynamics results from Minnhagen, 1981 the magnetic field dependence of PSSN was derived (Brandt et al., in preparation). i i 2 n n " " * 0 2) B B! 0.5 ( & ' R R TES N % # $ P. Minnhagen, Phys.Rev.B 23 (1981) D.Brandt et al., NIM A, in preparation

7 Field Dependence of Percolation Noise Using energy arguments it is possible to demonstrate a ~linear dependence of superconducting domain density on H 2. Using the dependence of R on sc domain density we deriver an approximate quantitative prediction for variation of noise with magnetic field (Brandt et al., in preparation). i n R # "! 0.9 rs i n R! 0.9 rs " " H H! 2.34! 2.34 D.Brandt et al., NIM A, in preparation

8 Magnetic Field Dependence of Noise The graph to the right shows data re-plotted from Ullom et al. This fits approximately with the expression we derived for Phase Slip Shot noise Excess Noise / Johnson Noise Noise vs B-field 5,00 4,00 3,00 2,00 1,00 0,00 0,00 50,00 100,00 150,00 200,00 experimental data (Ullom et al.) Phase Slip Shot Noise Percolation Noise Perpendicular field [mg] For fields >30 mg it does not agree with the expression derived for percolation noise Data points re-plotted from data recorded by Ullom et al. J. N. Ullom et al., Appl. Phys. Lett. 84 (2004) 4206

9 Geometry Dependence of Noise The magnitude of phase slip shot noise varies as ~area -0.5 Percolation noise should scale with device length-to-width ratio for small devices (smallest dimension << 500 domains) Percolation noise should be approximately independent of geometry for large devices Probabillty of complete sc channel [%] Percolation transition vs Aspect Ratio Percentage of SC domains [%] Simulation data recorded at Leicester width 20 height 100 width 40 height 100 width 100 height 100 width 150 height 100 width 400 height 25

10 Geometry Dependence of Noise The deposition of normal material geometries on top of the TES can have a strong effect on excess noise. Dense stripes normal to the bias current yield the best results Excess Noise / Johnson Noise Noise vs Geometry Dense full perpendicular stripes turn the device into a series of short wide TES which should be susceptible to Percolation Noise 0 dense full perp dense partial perp dense parallel islands standard J. N. Ullom et al., Appl. Phys. Lett. 84 (2004) 4206

11 Threshold Current Voss et al. report the excess noise to scale strongly with bias current/voltage. Takei et al. report an absence of excess noise for low (< 10 µa) bias current. Phase Slip Shot Noise explains threshold current with vortex dynamics Percolation Theory finds it difficult to explain the threshold current Bias current creates driving force Lattice defects and impurities create vortex pinning sites At sufficiently high driving forces vortices become unpinned R.F. Voss, C.M. Knoedler, P.M. Horn, Phys. Rev. Lett. 45 (1980) Y. Takei et al., NIM A 523 (2004) 134

12 Threshold Current - Predictions Vortices interact to form a glass phase According to Fangohr et al. the vortex glass undergoes a series of phase transitions with increasing driving force We predict a change in spectral composition of noise with phase change Graph taken from Fangohr et al. H. Fangohr et al., Phys. Rev. B. 64 (2001)

13 Validity of Models The Phase Slip Shot Noise model uses single vortex dynamics in the KTB-transition Therefore the model is valid for lower part of transition Percolation Noise is only valid in the percolation region (p sc ~ 56.3%) Probabillity of Superconducting Channel Percolation Transition Width Superconducting Domain Density [%] Therefore it is only valid near the centre of the transition

14 Summary Noise vs. Resistance Noise vs. Magnetic Field Noise vs. Geometry Threshold Current Validity of Model Phase Slip Shot Noise Predictions Low part of transition Percolation Noise Predictions Approximate agreement for fields < 30 mg Currently inexplicable by percolation theory High part of transition

15 Combination of Models Since noise is observed almost everywhere in the s-n transition both models are necessarily incomplete We conclude that a complete description of excess noise contains both models